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a_{n+1} = 3a_n-2a_{n-1} (V Soros Olympiad 1998-99 Round 3 10.6)

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May 26, 2024
algebraSequenceRecurrencerecurrence relations

Problem Statement

Find the formula for the general term of the sequence an, for which a1=1a_1 = 1, a2=3a_2 = 3, an+1=3an−2an−1a_{n+1} = 3a_n-2a_{n-1} (you need to express an in terms of nn).
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